Least Common Multiple of 31/14, 35/22, 77/68, 28/105

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Know Least Common Multiple of fractions 31/14, 35/22, 77/68, 28/105 quickly i.e. 47740 the smallest number that is divisible by all numbers by taking the help of LCM of Fractions Calculator.

Least Common Multiple (LCM) of 31/14, 35/22, 77/68, 28/105 is 47740.

LCM(31/14, 35/22, 77/68, 28/105) = 47740

LCM of 31/14, 35/22, 77/68, 28/105

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

LCM of:

Least Common Multiple of 31/14,35/22,77/68,28/105

Given numbers are 31/14,35/22,77/68,28/105

Formula to find LCM of Fractions is

LCM = LCM of Numerators/GCF of Denominators

As per the formula LCM of Fractions let’s split into two parts and find the LCM of Numerators and GCF of Denominators

In the given fractions LCM of Numerators means LCM of 31,35,77,28

Least Common Multiple of Numerators i.e. LCM of 31,35,77,28 is 47740.

GCF of Denominators means GCF of 14,22,68,105 as per the given fractions.

GCF of 14,22,68,105 is 1 as it is the largest common factor for these numbers.

Lets's calculate LCM of 31,35,77,28

LCM of Fractions 31/14,35/22,77/68,28/105 is 47740

7 31, 35, 77, 28
31, 5, 11, 4

∴ So the LCM of the given numbers is 7 x 31 x 5 x 11 x 4 = 47740

Least Common Multiple of 31,35,77,28 with GCF Formula

Least Common Multiple of 31,35,77,28 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 31,35,77,28 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(31,35,77,28) = 1

common factors(in case of two or more numbers have common factors) = 49

GCF(31,35,77,28) x common factors =1 x 49 = 49

LCM(31,35,77,28) = ( 31 × 35 × 77 × 28 ) / 49

LCM(31,35,77,28) = 2339260 / 49

LCM(31,35,77,28) = 47740


Lets's calculate GCF of 14,22,68,105

∴ So GCF of numbers is 1 because of no common factors present between them.

Thus LCM of Fractions = LCM of Numerators/GCF of Denominators = 47740/1

Therefore the LCM of Fractions 31/14,35/22,77/68,28/105 is 47740

Greatest Common Factor of 14,22,68,105 By Matching Biggest Common Factor Method

Greatest Common Factor of 14,22,68,105 By Matching Biggest Common Factor Method

Factors of 14

List of positive integer factors of 14 that divides 14 without a remainder.

1,2,7,14

Factors of 22

List of positive integer factors of 22 that divides 22 without a remainder.

1,2,11,22

Factors of 68

List of positive integer factors of 68 that divides 68 without a remainder.

1,2,4,17,34,68

Factors of 105

List of positive integer factors of 105 that divides 105 without a remainder.

1,3,5,7,15,21,35,105

Greatest Common Factor

We found the factors 14,22,68,105 . The biggest common factor number is the GCF number.
So the greatest common factor 14,22,68,105 is 1.


LCM of Fractions Calculation Examples

Here are some samples of LCM of Fractions calculations.

LCM of Fractions Calculation Examples

Here are some samples of LCM of Fractions calculations.

Frequently Asked Questions on Fractional LCM of 31/14, 35/22, 77/68, 28/105

1. How to find LCM in Fractions?

Answer: LCM of fractions can be found using the simple formula LCM of Fractions = LCM of Numerators/GCF of Denominators.

2. What is the LCM of Fractions for 31/14, 35/22, 77/68, 28/105?

Answer: LCM of Numerators as per given numbers 31/14, 35/22, 77/68, 28/105 is

LCM of Numerators i.e. for 31,35,77,28 is 47740

GCF of denominators i.e. for 14,22,68,105 is 1.

Thus, LCM of Fractions is 47740.Finally, LCM of Fractions for 31/14, 35/22, 77/68, 28/105 is 47740.